L I G
L I G
Fig. : •
Our excellent aftronomer, Dr. Bradley, has found nearly the fame velocity of Light, from his accurate obfervations, and molt ingenious theory, to account for fome apparent motions in the fixed ftars. Phil. Tranf. N° 406. See the article Star, Suppl.
To underftand this, it muft be premifed, that the fixed ftars are lum'mbus bodies, and at reft, with refpe£t to our plane- tary fyftem, from which they are vaftly remote. In this fyftem alfo the eaith is confidered as one of the planets, and moving about the fun.
Suppofe the fun reprefented in S, (Fig. 1.) and that the circle ABCD reprefents the path of the earth, or the ecliptic. At the center S fuppofe a perpendicular S P raifed to the plane of the ecliptic, and that this perpendicular paffes thro' any fixed ftar. If a fpe&ator were placed in S, he would fee the ftar in the fame perpendicular ; but if the fpe&ator paffes over the cir- cle A B C D, the diameter of which is fuppofed to bear a fenfible, tho' fmall pro- portion to the diftance of the ftar, it will be perceived to change its fituation in the heavens. For a fpc£tator in A would fee the ftar in the line A P a ; in C lie would fee the fame ftar in the line CPc; and fo in any other point of his progrefs : Whence it follows, that the ftar would feem to defcribe a circle in the heavens reprefent- ed by abed. If the diftance of the ftar was fo very great, that in refpe£t of it the diameter of the earth's orbit A C might be efteemed a point j in this cafe, the fore- faid circle would be entirely infenfible ; all the lines drawn from the points of the orbit to the ftar might pafs for perpendiculars to the plane of the ecliptic, and in appearance would correfpoad to the fame point in the heavens with the perpendicular in S, in which point the ftar Would always appear, if its light would reach us in an inftant. But if in this cafe, where the ftar is fo remote, the Light is fuppofed to be propagated from the ftar with a certain velocity, at the fame time that the earth proceeds in its orbit, the ftar will be (t^n in an oblique direction to the plane of the orbit ; becaufe of the motion compounded of the motion of Light t and that of the ipeftator.
,.......;.... Suppofe the Light to
y'^ move in the line E G
(Fig. 2.) making an angle with the line F G, in which the fpectator is carried along ; whom we fhall conceive placed in F. Let the velo- city of the fpe&a- tor be to the velocity of the Light, as F G toE G. While the fpectator moves along F G, the Light does the fame along E G ; and the particle of Lighti which is in Ei when the fpeftator is in F, enters the eye only when he arrives at G. Now the direction of the Light> with refpect to the eye, makes with the line F G the angle E F G. For if we conceive the line F E drawn, and to be carried with a parallel motion along with the eye, fo that in refpedt thereof it be at reft, while this continues moving, the Light will reach the eye in the direction of the (aid line ; for when the eye fhall be in/, the middle point between F and G, the transferred line will cut E G in its middle point g, to which the particle of Light has reached, and which is likewife the middle point of the transferred line f e. Wherefore the particle of Light, which was in E, in the extremity of the line E F, arrives at, and will enter the eye in the direction e g.
Let the angle E G F (Fig. 3.) be a right one, and EG to F G as the velocity of the Light to the velocity of the earth in its orbit j then E F G will be the angle, which the ray of Light entering the eye, makes with the plane in which the earth moves round the fun.
If the earth be in B, (Fig, 4.) it moves in the direction of the tangent to its otbit in this point ; that is, if we fuppofe the fpec- 1 tator in the fun, the direction of the earth's motion is parallel ' to S C ; and making the angle a S C equal to the angle E G F,
in the former figure, the line S a will reprefent the line in which the fpectator would fee the ftar.
In the fame manner when the earth is in D, the fpectator in the fun will fee the ftar in S r, the angles P Sr and P S a being equal ; and this line S a or S c, by its revolution about P S', would defcribe a cone, whofe bafe in the heavens would be a circle reprefenting the apparent path of the ftar thro' a whole year : Let us fup- pofe this circle to be a b c d, as in the A annexed figure.
When the ftar is not in the perpendicular to the plane of the ecliptic, but the line PS (Fig. 5.) is inclined to that plane, the lines which determine the apparent motion of the ftar in the hea- vens, will form cones, as in the caies already explained ; only they would be oblique, and in both cafes the apparent path of the ftar in the heavens would be deterni jied as above ; but in this Iaft cafe it would be an ellipfis, the greater diameter of which would be equal to the diameter of the circle abed of the former figures ; fo that knowing this ellipfis, the circle might eafily be found, which the ftar would defcribe, if placed in the perpendicular to the plane of the ecliptic.
Fig. 4.
Fig. 5-
The only way to determine, whether the ftars defcribe fuch elhpfes* is by obfervations ; in making which there are great difficulties, which however Mr. Bradley has with incompa- rable induftry furmounted._
Nothing can immediately be determined concerning the fore- faid elliptic motion. The diftance of the ftar from the pole of the world muff be meafured at different times of the year ; and from the different diftances, the elliptic motion is to be determined by calculation, allowing for the motion of tho pole itfelf during the fpace of time between the obfervations ; for the pole moves in a leffer circle, one degree of which it panes over in feventy years. Mr. Bradley, making all necef- fary allowances, obferved feveral ftars at different times of the year, whereby he immediately difcovered, that their diftances from the pole of the world varied ; and was con- vinced that this variation could not be attributed to the nuta- tion of the pole ; for he examined two ftars at equal diftan- ces from the pole, but fo oppofite, that the one ought to have receded from the pole as much as the other acceded to it, if the motion was in the pole itfelf. But this did not fall out fo ; for the change of the one ftar was double of that of the other; a proper allowance being always made for the pole's motion ariling from above the revolution. However this indefatigable obferver inferr'd from his obfervations, that the ftars in certain times receded from, and acceded to, the pole of the world with a motion eniirclv analogous to that which is performed in an ellipfis ; and alfo that they move in fuch curves, for each of which the motion in the fame little circle, as a bed, (Fig. 5.) anfwers, when the ftars are refer- red to the perpendicular in S to the plane of the ecliptic ■ and the diameter of this minute circle for them all is 4.0' i . It is plain from obfervations, to which of. the "above- mentioned caufes we are to afcribe the motion of the ftar. For if the firft takes place, the ftar would be carried from a to r, while the earth paffed over the part A B C of its orbit ; but this being contrary to obfervation, this cannot be the true caufe. But this change in the fituation of the ftar takes place according to the obfervations, while the earth de- scribes the part B C D of its orbit, which is iuft what the iecond caufe requires.
If both the caufes took place at the fame time, the arc, de- Icnbed by the earth, would differ from that indicated by ei- ther ot them ; befides, this concurrence of the caufes is con- trary to the obfervations ; unlefs perhaps it may be thought reafonable to attribute a little influence to the firft caufe, but fo veiy fmall a portion, as not to be fenfibly perceived in the obfervations.
From all which the following conclufions may be de- duced : 1. That the fecond caufe alone takes place here viz. That the diftance of the ftars is fo great, that the diame-
